x⁶ + 12 x⁵ + 60 x⁴ + 160 x³ + 240 x² + 192 x + 64
Step-by-step explanation:
(x + 2)^6
We begin by expounding the brackets;
x⁶ + x⁵ * 2¹ + x⁴ * 2² + x³ * 2³ + x² * 2⁴ + x¹ * 2⁵ + 2⁶
We then use the Pascal's triangle (attached) to put in the coefficients;
(1)x⁶ + (6) x⁵*2¹ + (15) x⁴*2² + (20) x³*2³ + (15) x²*2⁴ + (6) x*2⁵ + (1) 2⁶
We simplify and the final answer becomes;
= X⁶ + 12x⁵ + 60x⁴ + 160 x³ + 240 x² + 192 x + 64
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